curve #3884

y² + xy = x³ − 859118649195605190976469733301x + 291098433992187642875582346858662932831922081

a-invariants: [1, 0, 0, -859118649195605190976469733301, 291098433992187642875582346858662932831922081]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 205707713079649500111121632143097236465143277866450476078469324231130151383910
discriminant (Δ): 3975612729618021282280938915018312108164554687515390349979272276866350432966886608649830400
Faltings height: 16.1389
naive height: 218.3907
primes of bad reduction: 2, 3, 5, 7, 17, 37, 14971651, 20939930898184939, 4967475076934291338524271976735878724169987378991
regulator: 7941496293099381538006.626908274392919973082334882466501304897010104947401162205878
submitted by: 7fff-zip
submitted at: 2026-10-04 14:06:03 UTC
last updated: 2026-10-04 14:06:03 UTC

(-1021439265862720, 10145412181792093292561)
(14365517581836374, 1718293889997639248895803)
(485784804933052370/289, 294632014731757665951728167/4913)
(16785609094159313666/361, 68757484705782886966334382173/6859)
(142824118439405426, -53975068830246221675859913)
(23927182111647041354/529, -117016420830415592809443141071/12167)
(1288563157345186, -36381227011442800318553)
(647354147003426, -2495882436504912497113)
(321054528722611826/841, 105641511854776635276719683/24389)
(-128032323959685274/121, -5233890092167830460479743/1331)
(1039840668920648174/2809, 726239758212953017588325959/148877)
(16863218698263652034/2209, -68759040705446091458643313799/103823)
(168049065006617192546/249001, -537105535246990270584788836387/124251499)
(51864543855571010/121, -1685220933973927551388139/1331)
(1572314361857186, -53172607411935562594633)
(-326589186261014, 23169875643096479612167)
(1314606070950198702866/1985281, -9913444992363586217200173122537/2797260929)
(685969260365426, -4955291427749025855913)
(-28766316905776, 17770433581376977407713)
(5083954483589027866/7921, -1425774118978327609568676577/704969)
(-126780565590439870/121, 8520926494893641876996629/1331)
(-762238456956142, 22429567334034609489047)

X1008, t=4/39

last edited by 7fff-zip at 2026-10-04 14:06:03 UTC · history